Carrier-controlled ferromagnetism in SrTiO3

Magnetotransport and superconducting properties are investigated for uniformly La-doped SrTiO3 films and GdTiO3/SrTiO3 heterostructures, respectively. GdTiO3/SrTiO3 interfaces exhibit a high-density two-dimensional electron gas on the SrTiO3-side of the interface, while for the SrTiO3 films carriers are provided by the dopant atoms. Both types of samples exhibit ferromagnetism at low temperatures, as evidenced by a hysteresis in the magnetoresistance. For the uniformly doped SrTiO3 films, the Curie temperature is found to increase with doping and to coexist with superconductivity for carrier concentrations on the high-density side of the superconducting dome. The Curie temperature of the GdTiO3/SrTiO3 heterostructures scales with the thickness of the SrTiO3 quantum well. The results are used to construct a stability diagram for the ferromagnetic and superconducting phases of SrTiO3.

Unlike LaAlO 3 /SrTiO 3 , however, GdTiO 3 /SrTiO 3 interfaces grown by molecular beam epitaxy (MBE) exhibit mobile carrier densities that are remarkably well predicted by the electrostatic requirements of the compensation of the polar discontinuity at the interface [14]. Carrier densities are 3-4×10 14 cm -2 , or ~ ½ electron per surface unit cell, at each GdTiO 3 /SrTiO 3 interface for all heterostructures containing more than one unit cell of SrTiO 3 [14]. The staggered band alignment causes the mobile charge to reside in the SrTiO 3 , which is the wider band gap material [14]. These interfaces allow for doping of narrow SrTiO 3 quantum wells to extremely large and mobile carrier concentrations. For example, by sandwiching a few-unit-cellthick SrTiO 3 layer between two GdTiO 3 layers, carrier concentrations in the SrTiO 3 approach one electron per site, conditions under which electron correlation effects should appear [15,16].
Here we show that both types of samples, uniformly doped SrTiO 3 films and high-density two-dimensional electron gases at GdTiO 3 /SrTiO 3  concentrations of no more than ~ 1×10 16 cm -3 in these films [20]. We note that the carrier densities in the uniformly doped samples investigate here are slightly less than the dopant concentration, because of the well-known surface depletion of SrTiO 3 [21]. For the SrTiO 3 /GdTiO 3 heterostructures, the thickness of the SrTiO 3 layer was varied between 1 and 10 nm.
Ohmic contacts to the GdTiO 3 and SrTiO 3 layers were 300 nm Au/50 nm Ti and 300 nm Au/20 nm Ni/40 nm Al, respectively, with Au contact being the top-most layer in each case.
Magnetoresistance measurements were carried out in Van der Pauw geometry using a Physical  magnetoresistance is apparent at low temperatures (below 10 K), as has been previously reported for La-doped SrTiO 3 [22]. Concurrent with the appearance of negative magnetoresistance, R(B) becomes hysteretic, indicating ferromagnetism, when the magnetic field was in-plane and perpendicular to the current. We use the appearance of hysteresis to define the Curie temperature of the ferromagnetic transition, T Cm . We note that although extrinsic effects, the possibility of which is further discussed below, in ferromagnets may give rise to magnetoresistance hysteresis, the presence of a hysteresis nonetheless implies ferromagnetic ordering [23]. The shape of the hysteresis is very similar to that observed by Brinkman et al. for a LaAlO 3 /SrTiO 3 interface [3]; however, here it occurs at almost an order-of-magnitude higher temperature than in ref. [3].
Heterostructures with a single interface and 1-nm SrTiO 3 , which contain half the carrier density or less (sheet carrier densities of 4.6×10 14 cm -2 at room temperature and 1.9×10 14 cm -2 at 5 K; the latter corresponding to a 3D concentration of 1.9×10 21 cm -3 ), also show ferromagnetic hysteresis, albeit at a lower T Cm of about 3 K [ Fig. 1(b)]. Samples with thicker (2 nm) SrTiO 3 layers did not show any magnetoresistance hysteresis above 2 K. In addition to the hysteresis in R(B), all samples that exhibit hysteresis show an increase in resistance as the temperature is lowered, indicating a departure in the nature of conduction from conventional metallic systems [24]. For data from a sample with a slightly thinner SrTiO 3 layer, see ref. [24].
GdTiO 3 layers are ferrimagnetic [17,25] and it is therefore entirely conceivable that the magnetism of the carriers in the SrTiO 3 is induced by the proximity to the GdTiO 3 . However, the following observations can also be made: (i) ferromagnetism is absent in samples with SrTiO 3 layers that are thicker than 2 nm, despite similar sheet carrier densities and proximity to the GdTiO 3 ; (ii) the Curie temperature of GdTiO 3 is substantially higher (~ 20 K, see Fig. 2) than T Cm of any of the two-dimensional electron liquids investigated here; and (iii) ferromagnetism also appears in highly-doped bulk SrTiO 3 , when no GdTiO 3 layer is present, albeit at much lower temperatures, as will be discussed next.  Fig. 4a). This departure from the zero-resistance state is hysteretic (Fig. 4b). The temperature dependence of R(B) (Fig. 4a)  with La to higher carrier densities is possible [16,27], but to obtain the carrier densities of the quantum wells (up to 1×10 22 cm -3 in this study), the material would be more appropriately described as Sr-doped LaTiO 3 , which is a well-known antiferromagnet [28,29]. LaTiO 3 , up to Sr-doping concentration of ~10%, exhibits a weak, canted ferromagnetic moment [28].
Although even the highest La-doping concentration (~ 5% La doping) in this study is far from this regime, it is possible that locally such weak ferromagnetic correlations exist. Figure 5 summarizes the correlation between the 3D carrier concentration in SrTiO 3 and the ferromagnetic (this study) and superconducting transition temperatures (literature and this study). Data from both bulk and two-dimensional electron liquids is shown in the same graph.
For the uniformly doped films, a ferromagnetic phase stability region appears on the high-density side of the superconducting dome in the phase diagram, and, for a range of carrier concentrations, both phases coexist, as was evident in Fig. 4. The results from these samples provide evidence that ferromagnetic phase of SrTiO 3 at sufficiently high La dopant concentrations is likely not mediated by unintentional defects such as oxygen vacancies or Fe impurities. Impurity-related ferromagnetism typically persists to very high temperatures (see e.g., ref. [10]), which is different from what is observed here. The results from the uniformly doped films are consistent with recent reports of a field-induced Kondo effect in field-gated SrTiO 3 structures, which can be considered a precursor to the ferromagnetism at higher carrier densities [30]. When the data from the heterostructures and uniformly doped films are combined, as shown in Fig. 5, the ferromagnetism appears to depend strongly carrier concentration, even though carriers are introduced via two fundamentally different mechanisms (interface and conventional doping). However, more studies are needed to determine the degree to which the proximity to one or two GdTiO 3 interfaces, respectively, acts to increase the ferromagnetic transition temperature in the heterostructures, and to clarify the role of the Ladopants in the uniformly doped films.
Theoretical models of the ferromagnetism in doped SrTiO 3 should address the potential roles of band filling, Coulomb repulsion [31] and the coexistence with a superconducting state.
Theory should consider the importance of the role of the degree of filling of different bands and subbands in the SrTiO 3 [6], which are derived from the three degenerate t 2g d-orbitals of Ti [32], the role of strain and band degeneracy (note that all samples that exhibited ferromagnetism were grown on LSAT, causing compressive biaxial stress in the SrTiO 3 ) as well as the shape of the observed hysteresis, in particular the decrease in resistance as the magnetic field reaches the coercive field. Finally, the dependence of ferromagnetism on the quantum well thickness in the SrTiO 3 heterostructures implies that electric field gating may be used to modulate both ferromagnetism and superconductivity.      [33]). The sheet carrier densities of the quantum wells (n 2D ) were converted to 3D carrier concentrations (n 3D ) according to n 3D = n 2 D t cm !3 " # $ % , where t is the thickness of the quantum well and n 2D the carrier concentration determined from the Hall measurements at 5 K.  Figure S1 shows the magnetoresistance of a 4 nm GdTiO 3 /0.8 nm SrTiO 3 /4 nm GdTiO 3 /LSAT heterostructure at temperatures between 12 and 2 K. The carrier concentration for this sample at room temperature is 8.22×10 14 cm -2 and at 2 K it is 1.52×10 15 cm -2 , corresponding to a 3D carrier concentration of 1.9×10 22 cm -3 . Figure S1: magnetoresistance of a 4 nm GdTiO 3 /0.8 nm SrTiO 3 /4 nm GdTiO 3 /LSAT heterostructure at temperatures between 12 and 2 K. Hysteresis appears below ~ 10 K in sweeps with increasing and decreasing B, respectively (see arrows). Figure S2 shows the sheet resistances and Hall carrier concentrations of the GdTiO 3 /1-nm SrTiO 3 /LSAT and GdTiO 3 /1-nm SrTiO 3 / GdTiO 3 /LSAT heterostructures.